Tesi di LAUREA SPECIALISTICA Titolo Bayesian semiparametric approaches to mixed-effects models with an application in reliability analysis Data 2010-12-20 Autore/i Soriano, Jacopo Relatore Guglielmi, A. Relatore Argiento, R. Full text non disponibile Abstract In this work we provide a methodological study about Bayesian nonparametric random-effects models, and an application of these models in reliability. After a brief introduction to the nonparametric Bayesian approach, the construction of the normalized generalized gamma process (NGG) by normalization of a completely random measure is provided. This process is an ingredient of the models we will introduce later. Accelerated life testing (ALT) involves acceleration of failure times with the purpose of predicting the life-time of the product at normal use conditions. Data from an ALT can be analyzed by a so-called Accelerated Failure Time (AFT) model, where the dependence between the logarithm of the failure time is related to some explanatory variables. We analyze an AFT made by NASA on some pressure vessels, which are critical components of the Space Shuttle, via two semi-parametric Bayesian AFT models. The pressure vessels are wrapped with Kevlar from different spools and we treated the spool effect as random. In particular, we provide credibility intervals of some given quantiles of the failure-time distribution for a pressure vessel wrapped with fiber from a new random spool. In the first model the error is represented by a mixture of parametric distribution with a NGG mixing measure, while in the second one the random effects have a NGG process prior. For both models, we derived the analytical expressions of the full-conditional distributions needed to build a MCMC algorithm to sample from the posterior distribution; then we coded the algorithms in C and made numerical simulations. In particular, at each iteration of the first models algorithm, we sample a trajectory of the NGG process, while in the second model we implemented a Polya-urn scheme algorithm.